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Analysis of Times of Minima: the O-C Diagram

Once you have determined a time of minimum, you can submit it to be published (see Reporting). However, it can be very fruitful to look at the ToM in the context of an O-C diagram. This serves two purposes: it lets you look at how the star is behaving (i.e., is its period constant or changing?), and it provides a sanity check on your ToM. If your time of minimum really doesn't look right, in terms of previous data, you should revisit all your procedures and look for an error. Of course, it is completely unacceptable to change a result just because it doesn't fit, but if it causes you to backtrack and discover an error that you can correct, that is fine. Hopefully you will then avoid that error in the future.

So, what is an O-C diagram? It is very simple, and is just a specific example of a very general concept. You take your observations (the "O" in O-C), and subtract a calculated ("C") or predicted value, based on some model. In this context, the model is usually a linear ephemeris, i.e. a prediction of eclipse times that assumes a constant period. Different phenomena, such as a constant but incorrect period, period increasing or decreasing at a constant rate, or sudden period changes but constant period thereafter, have distinct patterns on the O-C diagrams.

Generating a light curve from a night of EB time-series observations is fun because you get to see a star doing something. The next step of adding your ToM to an O-C diagram lets you see evolution of a star system! See the Bibliography section for some excellent references on interpreting O-C diagrams.

A very easy way to see your datapoint on an O-C diagram is to use the BAV's LkDB site or the B.R.N.O.'s O-C Gateway page (see the "ToM Databases" page for links). At these sites you can bring up an O-C diagram for one of 1000s of stars, showing all the published data they have collected for that star, and then you can type in your ToM and see how it fits. You can also regenerate the O-C using a period that you specify. Furthermore, they let you download all the data they have for the star, so you can generate your own O-C using a spreadsheet or whatever program you choose.